The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0 X+2  0 X+2  0 3X 3X+2 3X+2  2  2 2X+2 2X+2  X  X 3X+2 3X+2 X+2 X+2  0  0  0  0 3X 3X  2  2 2X+2 2X+2  X  X 3X  X 3X 3X 2X 2X 2X 2X 2X 2X 2X 2X 3X 3X  X  X 2X+2 2X+2  2  2 3X+2 3X+2 X+2 X+2 2X+2 2X+2  2  2 3X+2 3X+2 X+2 X+2
 0  0 2X+2  0 2X 2X  2 2X  2 2X+2  2 2X+2  0 2X  2 2X+2  2 2X+2  0 2X  0 2X 2X+2  2  0 2X  2 2X+2  0 2X  2 2X+2  0 2X 2X+2  2 2X  0  2 2X+2 2X  0  2 2X+2 2X+2  2 2X  0 2X+2  2 2X  0 2X  0 2X+2  2 2X+2  2 2X  0 2X  0 2X+2  2
 0  0  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+1022x^64+1x^128

The gray image is a code over GF(2) with n=512, k=10 and d=256.
This code was found by Heurico 1.16 in 0.328 seconds.